Geometry_internal forces

1. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FUNDAMENTALS OF MATHEMATICS I

2. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

3. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
PREVIOUSLY ON MATHS 1...

4. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
GEOMETRY: VECTORS
EXAMPLE 1. INTERNAL FORCES IN BARS. JOINTS METHOD
EXAMPLE 2. INTERNAL FORCES IN BARS. JOINTS METHOD

5. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
FIRST MINUTE QUESTION
Username: First part of your CEU email
For example:
if your email is a.garcia245@uspceu.es
Your username will be a.garcia245
Password: SAME AS USERNAME

6. FIRST MINUTE QUESTION
Which of these sentences is true?
The magnitude of vector a is 5
A
B
C
D
The magnitude of vector a is 3
The magnitude of vector a is 4
The magnitude of vector a is 7

7. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WHAT IS A VECTOR?
Object that has both a magnitude and a direction.
The direction of the vector is determined by its orientation and its sense
The magnitude is the length of the vector.

8. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WHAT IS A VECTOR?
Object that has both a magnitude and a direction.
The direction of the vector is determined by its orientation and its sense
The orientation tells us the angle the vector makes with the cartesian coordinate axes
The magnitude is the length of the vector.
It is really useful to compute the dimension of the projections X, Y and Z of a vector

9. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS
IS THE MAGNITUDE OF a+b DIRECTLY THE ADDITION OF THE MAGNITUDES OF vector a AND vector b?
PARALLELOGRAM LAW (or Triangle Law)

10. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS
PARALLELOGRAM LAW (or Triangle Law)
MAGNITUDE OF vector c?

11. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS
MAGNITUDE OF VECTOR a+b+c+d?
BE CAREFUL WITH THE SIGNS!!!!

12. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
ADDITION OF VECTORS

13. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
SUBSTRACTION OF VECTORS?

14. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Bligh Lobb Sports Architecture
Millennium Stadium - Cardiff, UK – 1999 - [Bligh Lobb Sports Architecture

15. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Millennium Stadium - Cardiff, UK – 1999 - [Bligh Lobb Sports Architecture

16. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
The figure below is a simplified model of part of the structural system of the Cardiff
Millennium Stadium. Determine the sign and value of the forces at every bar.
*Assume all the forces have the direction of the bars.
*Assume every joint is in equilibibrium (addition of forces at each joint equals zero)

17. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
1.- How can I start?
2.- Do not forget: the magnitude is not enough!

18. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT B

19. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT B

20. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT E

21. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT E

22. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT F

23. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT F

24. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT A

25. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT A

26. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT C

27. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT C

28. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINTS METHOD. We analyze the equilibrium at every joint.
JOINT D

29. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT D

30. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

31. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
BE ORGANIZED!!!!
WATCH OUT THE SIGNS!!!!

32. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
WE KNOW IF THE RESULTS ARE CORRECT

33. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Today’s words?
https://www.menti.com/8cwme7e7ux
https://www.mentimeter.com/app

34. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
Bridge in Rodó Park. Tacuarembó. Uruguay

35. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
The figure below is a simplified model of the Bridge in Rodó Park,
Tacuarembó, Uruguay. Determine the sign and value of the forces at
every bar.
*Assume all the forces have the direction of the bars.
*Assume every joint is in equilibibrium (addition of forces at each joint
equals zero)

36. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
STUDENTS REP ELECTIONS
Angell Twyla 1
Bennis Amine 2
Caballero Jiménez Alicia Lishang 3
Canali Giovanni 4
Castell Carla 5
Cellier Malaxechevarria Claudia 6
Colorado Martínez Olivia 7
Domínguez Ayllón Claudia 8
Entrecanales Rivera Irene 9
Fernandez Fernandez Marina Iciar 10
Fernández Madrigal Catalina 11
Frezza Dessi 12
Frías González Fabiana 13
González D¿Alessandro Rodrigo 14
Hegab Tamim Ahmed Mohamed Mostafa 15
Hoth Brooklynn 16
Hurtado Summers Alvaro 17
Manzanares Casaseca Diego 18
Martin Ipiña Sofia 19
Medina Hernández Silvia 20
Mohamed Alansary Sama 21
Moreno De Redrojo Recio María Del Carmen 22
Nouri Laila 23
Ortiz Espinosa Mattheiu 24
Ozgur Ceren Nefise 25
Pardo De Francisco Cristina 26
Pira Natalia 27
Polvorosa Infesta Clara 28
Prados Gutiérrez Javier 29
Prieto Del Moral Guillermo 30
Putzu Chiara 31
Sanchez Jerez Adriana 32
Santos Fernández Rebeca 33
Sánchez Lodosa Eva 34
Soto Bergaz Gabriel 35
Tubol Vasyl 36
Vilaseca Martínez Javier 37
Wilde Jimenez Sebastian 38

37. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT A

38. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT A

39. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT B

40. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT B

41. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT D

42. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT D

43. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY

44. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT E

45. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY
JOINT E

46. FUNDAMENTOS MATEMÁTICOS DE LA ARQUITECTURA I
FUNDAMENTALS OF MATHEMATIC IN ARCHITECTURE I GEOMETRY